MinT - Best Known (126, 126+45, s)-Nets in Base 3

Best Known (126, 126+45, s)-Nets in Base 3

(126, 126+45, 288)-Net over F₃ — Constructive and digital

Digital (126, 171, 288)-net over F₃, using

t-expansion [i] based on digital (125, 171, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 57, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(126, 126+45, 614)-Net over F₃ — Digital

Digital (126, 171, 614)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+45, 21990)-Net in Base 3 — Upper bound on s

There is no (126, 171, 21991)-net in base 3, because

1 times m-reduction [i] would yield (126, 170, 21991)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1290 076958 861295 524947 563094 599658 204740 956198 186209 911859 424426 317018 228733 679717 > 3¹⁷⁰ [i]